A frequency-independent second-order framework for the formulation of experimental fluidelastic forces using hidden flow variables

The importance of fluidelastic forces in flow-excited vibrations is crucial, in view of their damaging potential. Flow-coupling coefficients are often experimentally obtained from vibration experiments, performed within a limited experimental frequency range. For any given flow velocity, these coefficients are typically frequency-dependent, as amply documented in the literature since the seminal work of Tanaka and Takahara. Such frequency dependence, which seems quite natural in view of the flows intricacies, not only is awkward for attempting physical interpretations, but also leads to numerical difficulties when performing time-domain computations. In this work, we address this problem by assuming that the measured fluidelastic forces encapsulate "hidden" (non-measured) dynamics of the coupled flow. This leads to the possibility of modelling the flow-structure coupled dynamics through conventional ordinary differential equations with constant parameters. The substructure analysis of such a model, augmented with a set of "hidden" flow variables, readily highlights an inevitability of the frequency-dependence found in the measured flow forces, when these are condensed at the measurement degrees of freedom. The formulation thus obtained clearly suggests the mathematical structure of the measured fluidelastic forces, in particular providing the formal justification for a modelling approach often used in unsteady aeroelasticity. Then, inspired by previous work in the fields of viscoelasticity and soil-structure interaction, we proceed by identifying adequate frequency-independent second-order flow-coupling matrices from the frequency-dependent experimental data, which is a challenging identification problem, even for the specific case of symmetric coupling detailed here. Finally, the developed concepts and procedures are applied to experimental results obtained at CEA-Saclay (France), for the fluidelastic interaction forces acting on a flexible tube within a rigid bundle, although the problem addressed embraces a much wider range of applications. The proposed flow modelling and identification approach shows significant potential in practical applications, with many definite advantages.